Question: Solve for $x$ and $y$ using substitution. ${2x-2y = -2}$ ${y = 5x+9}$
Solution: Since $y$ has already been solved for, substitute $5x+9$ for $y$ in the first equation. ${2x - 2}{(5x+9)}{= -2}$ Simplify and solve for $x$ $2x-10x - 18 = -2$ $-8x-18 = -2$ $-8x-18{+18} = -2{+18}$ $-8x = 16$ $\dfrac{-8x}{{-8}} = \dfrac{16}{{-8}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = 5x+9}\thinspace$ to find $y$ ${y = 5}{(-2)}{ + 9}$ $y = -10 + 9$ $y = -1$ You can also plug ${x = -2}$ into $\thinspace {2x-2y = -2}\thinspace$ and get the same answer for $y$ : ${2}{(-2)}{ - 2y = -2}$ ${y = -1}$